factorise x^2 + 185x +180
Answers
x2+8x=180
Two solutions were found :
x = 10
x = -18
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
x^2+8*x-(180)=0
Step by step solution :
Step 1 :
Trying to factor by splitting the middle term
1.1 Factoring x2+8x-180
The first term is, x2 its coefficient is 1 .
The middle term is, +8x its coefficient is 8 .
The last term, "the constant", is -180
Step-1 : Multiply the coefficient of the first term by the constant 1 • -180 = -180
Step-2 : Find two factors of -180 whose sum equals the coefficient of the middle term, which is 8 .
-180 + 1 = -179
-90 + 2 = -88
-60 + 3 = -57
-45 + 4 = -41
-36 + 5 = -31
-30 + 6 = -24
-20 + 9 = -11
-18 + 10 = -8
-15 + 12 = -3
-12 + 15 = 3
-10 + 18 = 8 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -10 and 18
x2 - 10x + 18x - 180
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-10)
Add up the last 2 terms, pulling out common factors :
18 • (x-10)
Step-5 : Add up the four terms of step 4 :
(x+18) • (x-10)
Which is the desired factorization
Equation at the end of step 1 :
(x + 18) • (x - 10) = 0
Step 2 :
Theory - Roots of a product :
2.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
Solving a Single Variable Equation :
2.2 Solve : x+18 = 0
Subtract 18 from both sides of the equation :
x = -18
Solving a Single Variable Equation :
2.3 Solve : x-10 = 0
Add 10 to both sides of the equation :
x = 10
Supplement : Solving Quadratic Equation Directly
Solving x2+8x-180 = 0 directly
Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula
Step-by-step explanation:
answer is 0 do disruption